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Register a new userTritium $beta$-decay in chiral effective field theory
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We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schru007fodinger equation with two- and three-nucleon potentials corresponding to either $chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.
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The beta decay of tritium in the form of molecular TT is the basis of sensitive experiments to measure neutrino mass. The final-state electronic, vibrational, and rotational excitations modify the beta spectrum significantly, and are obtained from theory. We report measurements of the branching ratios to specific ionization states for the isotopolog HT. Two earlier, concordant measurements gave branching ratios of HT to the bound HHe$^+$ ion of 89.5% and 93.2%, in sharp disagreement with the theoretical prediction of 55-57%, raising concerns about the theorys reliability in neutrino mass experiments. Our result, 56.5(6)%, is compatible with the theoretical expectation and disagrees strongly with the previous measurements.
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory, and accounts for cancellations between the contributions of irreducible diagrams and the contributions due to non-static corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. A complete set of contact terms for the axial charge up to the relevant order in the power counting is constructed.
Since the pioneering work of Weinberg, Chiral Effective Field Theory ($chi$EFT) has been widely and successfully utilized in nuclear physics to study many-nucleon interactions and associated electroweak currents. Nuclear $chi$EFT has now developed into an intense field of research and is applied to study light to medium mass nuclei. In this contribution, we focus on the development of electroweak currents from $chi$EFT and present applications to selected nuclear electroweak observables.
We discuss the contributions of lepton-number-violating sources to neutrinoless double beta decay ($0 ubetabeta$). Assuming that these sources arise at scales well above the electroweak scale, they can be described within an effective field theory. Here, we outline the steps required to express the $0 ubetabeta$ half-life in terms of the effective interactions, focusing on the dimension-five operator that induces a Majorana mass for the neutrinos. This process involves the evolution of the operators down to scales of a few GeV where they can be matched onto Chiral Perturbation Theory. The resulting Chiral Lagrangian can then used be to derive the lepton-number violating potential, which, in combination with many-body methods, gives the $0 ubetabeta$ half-life. We will show that consistent renormalization requires the inclusion of a new contact interaction at leading order in this potential. We also briefly comment on the constraints that can be set on the operators appearing beyond dimension five.
Chiral effective field theory ($chi$EFT), as originally proposed by Weinberg, promises a theoretical connection between low-energy nuclear interactions and quantum chromodynamics (QCD). However, the important property of renormalization-group (RG) invariance is not fulfilled in current implementations and its consequences for predicting atomic nuclei beyond two- and three-nucleon systems has remained unknown. In this work we present a first and systematic study of recent RG-invariant formulations of $chi$EFT and their predictions for the binding energies and other observables of selected nuclear systems with mass-numbers up to $A =16$. Specifically, we have carried out ab initio no-core shell-model and coupled cluster calculations of the ground-state energy of $^3$H, $^{3,4}$He, $^{6}$Li, and $^{16}$O using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order (NLO), where the subleading interactions are treated in perturbation theory. Our calculations indicate that RG-invariant and realistic predictions can be obtained for nuclei with mass number $A leq 4$. We find, however, that $^{16}$O is either unbound with respect to the four $alpha$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}$Li ground-state resides above the $alpha$-deuteron separation threshold. These results are in stark contrast with experimental data and point to either necessary fine-tuning of all relevant counterterms, or that current state-of-the-art RG-invariant PC schemes at LO in $chi$EFT lack necessary diagrams -- such as three-nucleon forces -- to realistically describe nuclei with mass number $A>4$.
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